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More Cantor set fun

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data

    I have two numbers: 509/729 and 511/729. I want to determine if they are in the Cantor set.

    3. The attempt at a solution

    I have:

    509/729 in base 3 is: 0.200212

    So this is not part of the cantor set because it can't be expanded in base 3 using only 0 and 2.

    ---------------------

    511/729 in base 3 is: 0.200221

    For this one, am I correct in saying that 0.200221 = 0.200220222...

    So, it can be expanded using only 0 and 2, and so is part of the cantor set?
     
  2. jcsd
  3. Nov 30, 2011 #2

    micromass

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    Indeed, both look good to me!!
     
  4. Nov 30, 2011 #3

    HallsofIvy

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    Since we form the Cantor set by removing open intervals, the endpoins of those intervals remain in the Cantor set. .02002213 is such an endpoint.
     
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